Question 1
The dream up product is 500 grams brown bread. The survey question was for this discussion was; how much are you willing to pay for a 500 grams loaf of brown bread? Using four prices ranges of between one and four dollars, a sample composing of ten friends and family members were asked how the survey question. In the excel sheet, the results of how many of the respondents were willing to pay a particular price for each of the four ranges was recorded. A scatter diagram of demand against prices was plotted to determine the relationship between price and quantity demanded. A histogram was also plotted on the excel sheet.
Observing the information in a graphic form provides more information because it shows the general trend of the data and the relationship. For example, in the scatter diagram of demand against prices on the excel sheet shows that the demand decreases as the product prices increases. This shows that demand and the product prices have an inverse relationship. Similarly, the histogram shows the trend and relationship between prices and quantity demanded at a glance. Secondly, observing the information in a graphic form provides more information about future movements. The graph can be extrapolated to determine what is expected next. For example, extrapolating the scatter diagram can be used to determine the demand at higher price levels such as 5 dollars. Lastly, graphs can provide information on data between ranges. For example, for the scatter diagram the corresponding demand for let us say 1.5 dollars, which lies between two price ranges, can easily be obtained.
Question 2
Correlation is a statistical tool used to establish how two items are related. For correlation to be used, variables in question must have some relationship. A firm uses its own records and information from other firms in its field of business. When a business firm finds the correlation of the items it is interested in, it can detect the trends of how they relate. These trends are what the firm uses in making forecasts of the future outlook of the business environment hence; the firm prepares the appropriate strategies for the future and makes decisions that befit the firm’s goals for the future. Using correlation, the firm decides how to implement the strategies and decisions made earlier. Using ideal mathematical equations in correlation, a firm can budget, cut costs and determine its future profits. Correlation values range between +1 for perfectly positive correlation and -1 perfectly negative correlation. Correlation of zero means the variables are not related.
Question 3
Good linear relationships between two points can be determined using linear regression. Regression is used when two variables; the dependent (unknown) variable and the independent (known) variable are available. Through a regression analysis, one is capable of predicting the dependent variable. Using quantitative regression, a formula can develop to establish the relationship between two variables. A regression line is then plotted, for every independent variable (x-axis); there is an expected dependent value (y-axis). From the regression equation, the dependent variable can also be predicted. The t-statistic which simply tests if the formula is valid determines the gradient of the line of regression. If the t-statistic is greater than zero, prediction of the dependent variable is possible.
If the t-statistic is zero or less, no relationship exists between the two variables, hence predictions are inaccurate. The square of the correlation coefficient is the determining coefficient. It ranges between zero and one. It can be directly interpreted as a part of the variance of the dependent variable that is represented in the regression equation. For example, 0.49 r-squared means 49% is explained in the regression analysis and the other 51% are not. A standard error estimate shows the Variability amount around the regression line points; it is also used to confirm the predictions made. Therefore, regression allows for the establishment of trends between complex factors and situations.
